RITZ METHOD IN THE DISCRETE APPROXIMATION OF DISPLACEMENTS FOR SLAB CALCULATION

Introduction: The FEM reduces the problem of structural analysis for various building structures to the formation and solution of a system of linear algebraic equations. For this purpose, there are techniques available for obtaining FE stiffness and flexibility matrices where the main structural deformation characteristics are taken into account. However, the FEM can also be considered as a special case of the Ritz method in the discrete approximation of the required functions. In the functional of full potential deformation energy with regard to the considered structure, all adopted stress-strain state characteristics are taken into account. Since it is difficult or impossible to find continuous approximation functions both in the classic version of the Ritz method and in the Bubnov–Galerkin method for some types of edge restraint in such building structures as beams, slabs, or shells, it is possible to use the Ritz method in the discrete approximation of the required functions (by analogy with the FEM). This paper presents a method of such calculations using slab calculations as an example. It is shown that, due to introducing some notations (operators), the process of finding th